Question

The computer that controls a bank's automatic teller machine crashes a mean of 0.6 times per day. What is the probability that, in any seven-day week, the computer will crash less than 3 times? Round your answer to four decimal places.

Answer 1

This is an application of POISSON DISTRIBUTION because of the following reasons.

1)Crashes are independent i.e one crash of machine does not affect another crash of machine.

2)Average rate of crash 0.6 is constant through out the time period.

3) There will be time gap between two successive crashes i.e events are not simultaneous.

Now we need to find probability that number of crashes in a week is less than 3 times.

Let X be the number of times that a machine crashes in a week.

For a week period , = 0.6×7 = 4.2

FORMULA: P (X=x) =( ^x . e^_) / x!

P (X < 3) = [(4.2^xi . e^-4.2) / xi !] where i takes 0,1,2

So, P (X <3) = 0.2102 (by using poisson distribution calculator)

Hence probability that machine crashes less than 3 times in any week = 0.2102   answer